Energy extraction from the Zero-Point

Field using Casimir cavities in the realm

of Stochastic Electrodynamics

Carlos Alberto de Oliveira Henriques, L.M.P. Fernandes, C.M.B. Monteiro, F.D. Amaro

LIBPhys – UCUniversity of Coimbra

July / 2015 - Seventh International Conference on Future Energy

Albuquerque, NM - USA

1. Introduction

2. Stochastic Electrodynamics

• Hydrogen atom in the free space

• Hydrogen atom inside a Casimir cavity

3. Methods to extract energy from the vacuum

4. Experimental setup

5. Results and discussion

6. Conclusions

7. Future work

Table of Contents

Introduction

2) Influence of the ZPF

• Cannot be directly observed (“virtual”)

• But its effects has been experimentally detected:

• The Lamb Shift

• The spontaneous emission

• The Casimir Force

• Casimir force between to plane reflectors:

• Originated by the electromagnetic differential pressure

• Theoretically it allows to extract energy from the ZPF, without violating any thermodynamic law

• Unfortunately, only works once, not in a continuous cycle

1) Zero-Point Energy (ZPE)

• Quantum Mechanics (QM) predicts:

Even at zero kelvin there is energy filling the vacuum

Zero Point Field fluctuations (ZPF) – imposed by the Uncertainty Principle

Introduction

4) Extracting energy from ZPF (continuous cycle)

1. For make energy flows → a lower energy state region is required

2. Such as the inside a Casimir cavity

3. The energy from outside must be stored with some mechanism

4. Inside the cavity this device can release the energy in excess

in QMZPF = “virtual”

photons

≠“real” photons

3) ZPF in our study

• Just the electromagnetic part of the ZPF

• We prefer to treat ZPF within the realm of classic mechanics

Classicmechanics

ZPF = real electromagnetic

waves

no distinctionsthe matter-ZPF interaction equal to the rest matter-radiation interactions

physics.aps.org

Introduction

5) Stochastic Electrodynamics (SED)

• Relativistic classic mechanics + ZPF

• Orbiting electrons → accelerated charges → radiates (spinning down towards the nucleus)

• But they also absorb energy form the ZPF

• Equilibrium between radiated and absorbed power → atomic stability

• Atoms could be that “mechanism”

Flow

The averaged radius is predetermined by the ZPF spectrum

1. Inside a Casimir cavity → the ZPF is modified

2. Atoms can undergo a shift in their states

3. Releasing Larmor radiation in that process

4. Just flow ground state atoms through Casimir cavities

Introduction

6) Goals

• Simulate the interaction between atoms and the ZPF

• Detect the possible shifts in the atomic states induced by Casimir Cavities

• Proof of concept: method to extract useful power from ZPF

7) Motivation

• ZPF → inexhaustible energy source: integrating up to the Plank frequency (1043 𝐻𝑧) VACUUM DENSITY 𝟏𝟎𝟏𝟏𝟑 𝑱 𝒎𝟑

• Green and available everywhere → ensuring the sustainability of future generations

• Study of the SED: a fundamental theory that still remains little explored (SED could explain the genesis of Quantum Mechanics)

Stochastic Electrodynamics (SED)

wave equations

of Maxwell

Newton’sequation of

motion(relativistic)

SED

Random Electromagnetic

background

𝝆 𝝎 =ℏ𝝎𝟑

𝟐𝝅𝟐𝒄𝟑1

2ℏω per mode

The only possible spectrum

(Lorentz invariant)

ℏ comes from experimental data

Nothing to do with QM

SED was able to explain:• In SED the quantization arises naturally• Casimir and van der Waals forces• Plank blackbody radiation• Unruh effect• Uncertainty principle

Some more controversial:• Inertia• Gravitation

But still lack many systems, such as the atom inside a Casimir cavity…

Classically: matter is continually radiating(radiation reaction)

Radiation from distant matter

=ZPF

ZPF compensates energy losses

→ stability

SED – Hydrogen atom (H)

𝑚𝑑2𝒓

𝑑𝑡2= −

𝑒2𝒓

4𝜋𝜀0 𝒓3+

2𝑒2

3𝑐31

4𝜋𝜀0

𝑑3𝒓

𝑑𝑡3− 𝑒 𝑬 𝒓 𝑡 , 𝑡 +

𝑑𝒓

𝑑𝑡× 𝑩 𝒓 𝑡 , 𝑡

𝑬𝑍𝑃𝐹 𝒓, 𝑡 =1

𝐿𝑥𝐿𝑦𝐿𝑧

𝑛𝑥,𝑛𝑦,𝑛𝑧=−∞

∞

𝜆=1,2

𝜺𝒌𝒏,𝜆 𝐴𝒌𝒏,𝜆 cos 𝒌𝒏 ∙ 𝒓 − 𝜔𝒏𝑡 + 𝐵𝒌𝒏,𝜆 sin 𝒌𝒏 ∙ 𝒓 − 𝜔𝒏𝑡

1

𝑐 𝒌𝒏 × 𝜺𝒌𝒏,𝜆

𝒌𝒏 = 2𝜋𝑛𝑥

𝐿𝑥 𝒙 +

𝑛𝑦

𝐿𝑦 𝒚 +

𝑛𝑧

𝐿𝑧 𝒛

𝜔𝒏 = 𝑐|𝒌𝒏|

𝑩𝑍𝑃𝐹 𝒓, 𝑡

CoulombRadiation reaction ZPF force from 𝑬 and 𝑩

Gauss distribution

Mean = 0

Variance =ℏ𝜔𝒏

2𝜀0

integers

Cavity dimensions(big for free

space)

Newton’s second law of motion for 𝒆− in 𝑯 (non-relativistic)

Expansion of plane waves (Maxwell’s equations in a bounded space)

SED – H in the free space - simulations

Approximations to speed up the numerical integration originally proposed by Cole and Zou (2003):

• To force a 2D orbit in 𝑥𝑦:

1. Narrow cavity 𝐿𝑥 = 𝐿𝑦= 3.74 𝑛𝑚 and 𝐿𝑦= 𝟒. 𝟏 𝒎𝒎

2. No 𝐵, and 𝐸 waves in only one direction 𝑧

• At each iteration: just the waves in resonance with 𝑟 within a frequency window 𝑟 ± 0.03𝑟

• No waves for 𝑟 below 𝑟𝑚𝑖𝑛 = 1 × 10−11

𝑥𝑦

𝑧Long enoughto consider it in free space

The atom was never fully described by SED

Difficulties in the analytical solving, owing to the non-linear Coulomb potential

solution: numerical integration

SED – H in the free space - simulations

• In order to get a better statistics , 261 simulations were carried out (Cole and Zou (2013) made 11 simulations)

• Only 64 reached the final time = 5 × 10−11 s (longer than Cole and Zou)

Comparing the classic decay with the SED’s result the ZPF seems to avoid da atomic colapse

Extremelly elliptic orbits randomness decreased

← Continuously rising orbits(spontaneous ionization)

Some runs were not so good:

SED – H in the free space - simulations

Radius distribution of the 𝑒− from 32 summed simulations

1 2

3 4

• Histograms of all simulations summed (as Cole and Zou done)

• It’s included in each histogram only the radius up to a certain time limit

• This time limit increases from 1 to 4

• If there is no trends over time, this is just the same as increasing the statistics

Longer time limit greaterstatistics, but...

Diverges from QMIs the averaged radius time

dependent?

The radius distribution from SED converges to

the QM’s prediction (blue curve)

SED – H in the free space - simulations

• Average radius as function of time (blue line) there is in fact a trend over time towards spontaneous ionization – are the electron absorbing excess of power from the ZPF?

Possible causes:

1) The computational model or even the SED are wrong

2) The utilization of minimum radius 𝑟𝑚𝑖𝑛 = 0.1 Å

3) The use of only the waves in resonance with the orbit

(frequency window)

4) The use of only 𝐸 waves in just one direction imposed by

the cavity dimensions if 𝐿𝑥 and 𝐿𝑦 are changed, the

model should still describe the free space, however

owing to the normalization constant 1 𝐿𝑥𝐿𝑦𝐿𝑧 the

amplitude of the waves will be changed too

Simulations for two diferent 𝐿𝑥and 𝐿𝑦 as we suspected this

parameters have a strong influence on the results, so it

could be the problem

SED – H in the free space - simulations

1) In the case where 𝐿𝑥 and 𝐿𝑦 were decreased, the 𝑟𝑚𝑖𝑛 was consequently

decreased for 0.43 × 10−11 → There were even more simulations reaching the 𝑟𝑚𝑖𝑛 most likely the lower radius limit is not the problem

2) We performed an additional simulation where all the waves except the ones in resonance were included

This waves have also a great influence in the radius of the orbit the frequency window could be the problem

Conclusion: The origin of the problem could be a combination of these discrepancies

Interesting note: owing to a bug in the code we generated waves just in 𝑥 and traveling in only one orientation,

where the best match with QM was achieved

SED – H inside a Casimir cavity

To solve the discrepancies found in the Cole and Zou’s model:

1D ZPF 3D ZPF

• Much more computationally heavy

• It allows to simulate the Hydrogen in 3D

We computed the equilibrium radius (𝑟𝑒𝑞) of

the orbit for cavity case using the 3D ZPF :

It was not possible yet to validate this model for the free space with our actual computational resources

↑ 3D Hydrogen inside a cavity

Unfortunately these results are not reliable due to the many considerations we have done:

• We used the analytical equation of the absorbed power according to the Harmonic Oscillator approximation

• We used the radiated power characteristic of the free space

← 𝒓𝒆𝒒 decreases as the edge (𝑳) of the cubic cavity decreases

Methods to extract energy from the vacuum

Casimir cavity

Flow

Many questions and hypotheses…

If there are shifts, how will they occur?

1. Progressively in a spiral-like decay orbit, emitting Larmor radiation at the electron spinning frequency

2. In a transition-like process, most likely with a characteristic half-life time and emitting radiation whose frequency is related to the shift

?Ground state reduction method (without excitation):

• Ground state atoms flowing through Casimir cavities

• May be necessary supress the ZPF’s modes in resonance with the valence orbits

Methods to extract energy from the vacuum

Possible causes…

1) The shifts were outside the studied energy ranges study other energy ranges (visible and UV)

2) There is no shift in the ground state try excited states

3) The shift is hard to detect try excited states

4) A transition between states is required to the shifts take place search for an energy gain in transitions

5) There is no shift at all ☹

Ground state reduction method (state of the art)

• Moddel and Dmitriyeva’s experimental data was inconclusive (IR-region)

• Puthoff was not able to detect the 𝐻2 molecular ground state shift

Owning to the fluctuation-dissipation theorem no major shiftin the Harmonic Oscillator’s equilibrium state is expected, only small radiative correctionsHowever HO ≠ atoms

1. Waves can be themselves supressed inside the cavity

2. Their energy can be hard to distinguish from thermal noise

In excited states a higher shift is expected since the electrons’ orbits have lower frequencies

Transition + shift have a smaller wavelength than the shift alone

Methods to extract energy from the vacuum

Excite-Outside-Method (EO)

If the shift only happens through a transition…

EI-method: gain = ground-state shift

Excite-Inside-Method (EI)

With excitation:

Radiation emitted directly from the shift

Energy gains in atomic transitions

If there is no need for a transition and most likely the shift is immediate as the atom enters…

EO-method: gain = excited-state shift (higher)

Flowing the excited atoms through the cavities (we did not test this hypothesis)

Experimental setup

Casimir cavityMetals become bad reflectors above their plasma frequency

Aluminium is the better choice since its reflectance is still high at the VUV region (~90% @ 200 nm)

SEM photos (d=100 nm)↓ 20 000 × ↓ 100 000 ×

We used: Nuclepore Track-Etched

Polycarbonate nano-porous

membranes coated with Al

Pores diameter (d): 50 and 100 nm

Thickness: 7 - 20 μm

Differential pressure: 0.69 bar

Pore density: 105 - 6 × 108 cm−2

Experimental setup

The MC 1 excites the atoms with 𝝎𝟎 and the MC 2 records the emitted radiation, when a 𝝎𝒄 > 𝝎𝟎 is detected, there was an energy gain

Can be used with EI-method or EO-method

Designed to detect energy gains in atomic transitions

Turning off the MC1, we can also detect the emitted radiation from ground state flowing atoms (Ground state reduction method)

PMT: 160 - 650 𝑛𝑚, also operable down to ~ 115 nm (less sensitive)

MC1 and MC2: ~30 - 550 𝑛𝑚

Lamp: deuterium, continuous spectrum 115 - 370 𝑛𝑚

Chamber: stainless steel vacuum system, pumped with two turbo-molecular

Gas: Xenon, because is the heavier noble gas and have the resonance transition of lower energy (3P1 𝜆 ≈ 147. 1 𝑛𝑚)

Data acquisition: a Multi-Channel Analyser

Experimental setup

MembraneOur instrumentation

With excitation (pores = 100 nm):

1. Exciting: in the Xe resonance transition (λ = 147. 1 𝑛𝑚) testing the shift in the ground state (Excite-Outside-Method)

Scanning: from 107 – 147 𝑛𝑚

2. Exciting: in three different wavelengths (λ = 250.2 𝑛𝑚, 210.2 𝑛𝑚, 165.2 𝑛𝑚) higher than the Xe resonance transition testing the shift in the excited state (Excite-Inside-Method)

Scanning: from each emitted λ + 20 𝑛𝑚, to 130 𝑛𝑚

Results and Discussion

No radiation detected, neither for λ < 147.1, nor for excited λ = 147.1 𝑛𝑚 itself

Problems found: PMT’s bad sensibility below

160 𝑛𝑚

+radiation losses in: MCs, Xe,

solid angle and windows

No radiation detected for λ = 147.1 𝑛𝑚, and from all excited λ, only 250.2 𝑛𝑚 was detected

Poor sensitivity(evident in the non-detection of

the excited λ)

So, we did not consider these results conclusive

Results and Discussion

Without excitation – spectroscopy (pores = 100 nm):

• With Xe flowing through the membrane, green line (differential pressure ~0.4 𝑚𝑏𝑎𝑟)

• Two background spectrums (red and blue lines), one being made before and other after the main experiment

Smooth curves adjusted to the experimental data to facilitate the visualization

No radiation detected

At this time the sensitivity was greater, even so, it was not optimal

↑ photo-counting as a function of the differential pressure

Results and Discussion

Without MCs, with the PMT assembled some 𝑚𝑚 away from the membrane (at the gas entrance side)

• The flow increases with the differential pressure (with the exit side being always in vacuum)

• Comparing with 3 backgrounds

• No radiation at all was detected

Great sensitivity from 160 - 650 𝒏𝒎

Without excitation – quantitative (pores = 50 nm):

Conclusions

Experimental research:

1) The tests using preliminary excitation were not conclusive since our instrumentation showed a poor sensitivity within the studied energy ranges

2) If ground state Xe atoms radiates as they enter into Casimir cavities the radiation’s energy is not in the ranges:

• 2.3 – 7.8 eV for pores =100 nm, low sensitivity

• 1.9 – 7.8 eV for pores = 50 nm, high sensitivity

Computational research:

1) Cole and Zou’s model is not suitable to describe the H in free space:

• For longer integration times the radius distribution diverges from the QM’s prediction

• The averaged radius have a continuous trend to outer orbits

• The narrow cavity approximation (𝐿𝑥, 𝐿𝑦 - short and 𝐿𝑧 - large) is not proper for

the free space

Future research

Computational research:

• Validate the 3D-model for the free-space and then use it for cavities (using the modified radiation reaction force)

• Simulate the excited states and atomic transitions

Experimental research:

• To increase the sensitivity:

Using other atoms whose transitions have lower energies

Improve all the optical system: lenses, geometry, windows, PMT…

• Use nano-porous membranes integrally made of metal

• Explore the shifts in the ionization and molecular dissociation energies

Future research – new concepts

The orbit is strongly affected by ZPF’s modes outside the resonance most likely, these modes also perform positive work on the electron

Using proper cavities, radiation, magnetic/electric fields or even a specific electromechanical

device, a motion with a fixed frequency could be achieved

an excess of radiation at such frequency would be detected since part of the absorbed energy

comes from other frequencies

We showed that the ZPF can increase the averaged potential and kinetic energy of the orbiting electrons

We can use this principle to make the electrons move against the electric potential in a proper device

𝐸

𝐵

−+𝑖

𝐿𝑂𝐴𝐷

𝑖

Just an idea:

1. The electrons leave the positive pole by thermionic emission

2. A magnetic field make them to curve and get in orbit around the positive pole

3. Due to the ZPF, the average orbit radius increases resulting in a motion of the electrons from the positive pole to the negative one

Questions

“Only those who attempt the absurd will achieve the impossible.”

Albert Einstein

References

• Henriques, Carlos Alberto de Oliveira. “Study of atomic energy shifts induced by Casimir cavities.” MSc Thesis, University of Coimbra, 2014. Web. <http://hdl.handle.net/10316/28082>

• Davis, E. W., et al. "Review of experimental concepts for studying the quantum vacuum field." Space Technology and Applications International Forum- Staif 2006. Vol. 813. 2006.

• Dmitriyeva, Olga, and Garret Moddel. "Test of zero-point energy emission from gases flowing through Casimir cavities." Physics Procedia 38 (2012): 8-17.

• Cole, Daniel C., and Harold E. Puthoff. "Extracting energy and heat from the vacuum." Physical Review E 48.2 (1993): 1562.

• Boyer, Timothy H. "Random electrodynamics: The theory of classical electrodynamics with classical electromagnetic zero-point radiation." Physical Review D 11.4 (1975): 790.

• Puthoff, Harold E. "Ground state of hydrogen as a zero-point-fluctuation-determined state." Physical Review D 35.10 (1987): 3266.

• Huang, Wayne Cheng-Wei, and Herman Batelaan. "Dynamics Underlying the Gaussian Distribution of the Classical Harmonic Oscillator in Zero-Point Radiation." Journal of Computational Methods in Physics 2013 (2013).

• Cole, Daniel C., and Yi Zou. "Quantum mechanical ground state of hydrogen obtained from classical electrodynamics." Physics Letters A 317.1 (2003): 14-20.

• França, Humberto de Menezes, Trevor W. Marshall, and E. Santos. "Spontaneous emission in confined space according to stochastic electrodynamics." Physical Review A 45.9 (1992): 6436.